Hooke's law and Elastic Potential Energy

A spring is compressed 0.035 m inside a dart gun. The spring constant (k) is 500 N/m. How much energy is stored in the spring?

0.31 J

A 5 kg ball is dropped from a height of 3 meters onto a vertical spring. The spring constant is 800 N/m. How far will the spring compress?

0.61 m

A vertical spring with a spring constant of 900 N/m has been compressed 0.8 meter. The spring is used to launch a 2 kg ball straight up into the air. How high will the ball go?

14.7 m

An archer used 2,000 J of energy to stretch a bow string 0.15 m. What is the spring constant (k) of the bow string?

180,000 N/m

A compressed spring has 20,000 J of energy stored in it. The spring constant (k) is 1,500 N/m. How far was the spring compressed?

5.16 m

A spring is stretched 0.2 meters. The spring constant (k) of the spring is 2500 N/m. How much energy is stored in the spring?

50 J

Formula for Hooke's Law.

F=kx

Unit for force

Newtons

Spring constant is measured in _____

Newtons/m, because it describes the force needed to stretch/compress the spring by a meter.

State Hooke's Law using words.

The amount of force applied to a spring is proportional to how much it stretches or compresses

Displacement (x)

The distance (measured in meters) the spring stretches or compresses from its normal state or equilibrium. Displacement includes direction, because it is a VECTOR.

Applied force (F)

The force that is applied to the spring to stretch or compress it.

Spring

any elastic object able to store energy (spring, rubber band, popper, slingshot...)

Small spring constant

loose spring, like a slinky or the alien popper

Unit for displacement

meters

Large spring constant

rigid spring, like the one on your car or on a trampoline